Abstract

BROOKHAVEN SCIENCE ASSOCIATES

Abstract

Vibrating Wire R&D for Magnet Alignment

Animesh Jain, NSLS-II Project The alignment tolerance for a string of magnets on a girder in NSLS-II is ±30 microns. Such a level of alignment is

difficult to meet with manufacturing tolerances and survey alone. It was decided early in the project to use the vibrating wire technique to align magnets on a girder for NSLS-II. This technique was developed at Cornell, and good measurement resolution of ~few microns was already demonstrated in quadrupoles. However, there were no systematic studies available to demonstrate the absolute accuracy of the measured centers. Similarly, very little work was done in applying this technique to sextupoles. In view of this, an R&D program was initiated at NSLS-II in early 2007. Extensive work was carried out to identify various sources of errors and means were devised to minimize such errors. A brief description of various aspects studied is presented in this talk. This R&D work culminated in building a state-of-the-art vibrating wire measurement system for NSLS-II and demonstration of absolute accuracy of ~±5 microns for sextupoles. The system is now fully operational for production measurements and over 1/3 of all the multipole girders have already been aligned to well under the required tolerance using this system.

*Work performed under auspices of the United States Department of Energy, under contract DE-AC02-98CH10886

1


Vibrating Wire R&D for Magnet Alignment

Magnet WorkshopApril 11-12, 2012

Animesh Jain for the NSLS-II magnet team


NSLS-II Magnet Workshop: April 11-12, 20123

Introduction• For optimum performance, the magnetic axes of quadrupoles

and sextupoles in NSLS-II should be aligned to better than ±30 microns.

• It is difficult to achieve the required accuracy using magnet fiducialization, coupled with optical survey.

• It is difficult, and expensive, to maintain the required machining and assembly tolerances in a long support structure (~5 m) holding several magnets.

• It is desirable to achieve the required alignment using direct magnetic measurements in a string of magnets.

• The vibrating wire technique, developed at Cornell, was deemed to be the most appropriate for this task.



Magnet Alignment R&D• Although the vibrating wire technique had been used in the past

for quadrupole measurements, very little work had been done in sextupoles. Also, little was known about absolute accuracy.

• An R&D program was initiated to further develop the technique at BNL and demonstrate the required accuracy for both quadrupoles and sextupoles.

• Good measurement reproducibility has been achieved as a result of several improvements made over the course of this R&D program, which started in January, 2007.

• The technique has now been used successfully to precision align 30 girders for NSLS-II storage ring.

• A sustained throughput of 2 girders per week is achieved.



The Vibrating Wire Technique: Basics

• An AC current is passed through a wire stretched axially in the magnet.• Any transverse field at the wire location exerts a periodic force on the wire, thus

exciting vibrations.• The vibrations are enhanced if the driving frequency is close to one of the

resonant frequencies, giving high sensitivity. • The vibration amplitudes are studied as a function of wire offset to determine the

transverse field profile, from which the magnetic axis can be derived.

X-YStage

X-YStage

X Y

Weight

Wire carryingsinusoidal current

MagnetMover

Magnet

WireVibrationSensors



Main Features of the BNL Vibrating Wire System• Aerotech ATS03005 stages for wire movement

(0.1 micron resolution; 2.5 micron/25 mm accuracy).

• Wire ends are defined by stainless steel V-notches.

• Set of 7 fiducials at each end to locate the V-notches.

• A pair of X-Y wire vibration sensors at each end of the wire. Allows two independent, simultaneous measurements for data verification and redundancy.

• Computer controlled piezo stages to recenter wire sensors at each scan position to minimize non-linear effects.

• Completely rewritten acquisition and analysis software with scripting support for flexibility in experiment control.



Wire End Support (V-notch)

Fiducials relate the wire ends to the overall girder coordinate system.

Stainless V-notch

Fiducial nests (7)

Holes to help locate the notch relative to fiducials

A V-notch with radius much smaller than the wire was chosen. The wire position is thus insensitive to the actual radius of the V-notch.



Wire Vibration Sensors

As the wire is moved horizontally or vertically, the position of the wire relative to the sensor changes slightly (~ a few microns) due to imperfections in the stage motion. This causes a change in the operating point of the sensor.

An automated piezo stage was added to keep the wire “centered” in the sensors during a scan.

Coarse manual adjustment in orthogonal axis

X-Sensor

Fine, automated adjustment along measurement axis using piezo stages

Y-Sensor

The wire motion sensors are inexpensive photointerrupters(Model GP1S094HCZ0F)

A pair of sensors is located on both ends of the wire, thus allowing two simultaneous measurements.



Complete Wire Mover AssemblyCamera to ensure wire is correctly seated in the notch

Light Shades to reduce noise from stray light

V-notch holder with fiducials

A similar assembly is present at the other end of the wire, except that the pulley and weight are replaced by a fixed wire end.



Alignment Issues Studied• Wire sag correction (presented at IMMW15)• Detector sensitivity to orthogonal motion• Sensitivity to Yaw/Pitch of magnets• Accuracy of quadrupole center measurement• Accuracy of sextupole center measurement• Background field correction• Ability to precisely move magnets and secure to the girder.• Reproducibility of the girder vertical profile.• Stability of magnet alignment during transportation and

handling of the girder.



Detector Sensitivity to Orthogonal Motion

Measured signal is contaminated by sensitivity to motion along the orthogonal axis, thus causing errors in the measurement of magnetic center.

Response of X1 & Y1 Detectors to X1 Stage Motion

y = -0.00026x - 0.00070y = 0.0137x + 0.0089

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

-50 -40 -30 -20 -10 0 10 20 30 40 50Wire X1-Motion (microns)

X1

Sens

or O

utpu

t (V

)

-0.020

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

0.020

Y1

Sens

or O

utpu

t (V

)

Sensor X1Sensor Y1

18-Dec-08

A rigorous analysis has shown that the error in horizontal/vertical center is minimized if wire is scanned at the vertical/horizontal center in both quadrupoles and sextupoles. This implies that a rough center must be found first before the final scan.



Resonant Mode to Use: Yaw/Pitch Sensitivity

• Should have a maxima near the axial center of the magnet being measured.

• Preferably even numbered modes should be used to avoid contribution from any axially uniform background fields (e.g. earth’s field).

• It may be impractical to find a mode with maxima exactly at the axial center for every magnet on the girder. This causes sensitivity to yaw and pitch.

• One should choose a mode that minimizes sensitivity to yaw and pitch without sacrificing signal strength.



Sensitivity to Yaw and Pitch

Signal for mode = n is proportional to Byn(for a given detector position)

In a quadrupole magnet with offset x0 and yaw angle , located at z = zmag:

Error in center determination due to yaw:

A similar analysis for sextupoles is much more tedious, but the same expression for x0 is obtained in the end!

A similar expression applies to vertical offset and pitch angle.

zmag = magnet axial position; G = Gradient

Lmag = magnetic length

L = wire length



Yaw/Pitch Sensitivity in Quad MeasurementsYaw/Pitch Sensitivity in Quad Measurements

-40

-30

-20

-10

0

10

20

30

40

0 2 4 6 8 10 12 14 16Mode Number

Yaw

/Pitc

h Se

nsiti

vity

(m

icro

n/m

rad)

m 23.0m 98.3

m 27.7

mag

magLzL



Sextupole Measurements Using By and Bx

• Obtaining centers from By vs. x and By vs. y plots uses only one set of sensors, and requires quadratic fits.

• One could also use scans of Bx vs. x (or y) for various values of y (or x). These plots are expected to be linear with slopes proportional to offsets in y (or x) direction.

• Doing three such scans allows to obtain centers from both Bx and By data. With 2 sets of sensors, one gets four values of magnetic center.

2

20

20

3)()(

refy

RyyxxBB

2

003

))((2ref

xR

yyxxBB



Yet Another Way to Measure Sextupoles

Fit measured data to a truncated Fourier Series, giving quadrupole and sextupole terms.

Both X and Y Centers can be obtained using any of the 4 detectors in a single scan.

Circular Scan (R = 1 mm) in SLS Sextupole at 100A

-60

-40

-20

0

20

40

60

0 45 90 135 180 225 270 315 360Angle (deg.)

Sign

al (a

rbitr

ary

units

)

X1 X1Fit Y1 Y1FitX2 X2Fit Y2 Y2Fit

19-Mar-2008Uncorrected



Comparison of Sextupole Data Using Bx and By

Summary of Sextupole Center Measurements in SR110 at 100A19-Mar-2008: Comparison of Circular and Linear Scan Results

X_Center(mm)

Y_Center(mm)

X_Center(mm)

Y_Center(mm)

X_Center(mm)

Y_Center(mm)

1 X1 (B_y) 13.7 -30.8 -155.1 -31.3 -168.8 -0.52 Y1 (B_x) 8.3 -31.8 -160.8 -32.5 -169.1 -0.73 X2 (B_y) 13.7 -34.1 -154.5 -33.1 -168.3 1.04 Y2 (B_x) 8.7 -31.1 -160.1 -31.5 -168.8 -0.45 X1 (B_y) 10.0 -31.5 -160.9 -32.5 -170.9 -1.06 Y1 (B_x) 10.8 -32.9 -160.0 -35.0 -170.8 -2.17 X2 (B_y) 9.4 -31.6 -161.5 -32.9 -170.9 -1.38 Y2 (B_x) 10.1 -32.1 -160.6 -30.5 -170.7 1.6

10.6 -32.0 -159.2 -32.4 -169.8 -0.42.1 1.1 2.8 1.4 1.1 1.211.1 -31.9 -157.6 -32.1 -168.7 -0.23.0 1.5 3.3 0.8 0.3 0.810.1 -32.0 -160.7 -32.7 -170.8 -0.70.6 0.7 0.6 1.9 0.1 1.61.0 0.1 3.1 0.6 2.1 0.5

Uncorrected Background Corrected Correction Needed inMethodNumber Scan Type Sensor

Used

CIRCULAR(single scan;

25 points)

LINEAR(6 scans;7 points

each)

Mean of all 8 methods:

Std. Deviation of all 8 methods:

Circular to Linear Scan Diff.:

Mean of Circular Scan Data:

Std. Deviation of Circular Scan:

Mean of Linear Scans:

Std. Deviation of Linear Scans:

Consistency comparable to quadrupole measurements is obtained in more recent data.



Issue of Background Fields in Sextupole Meas.

• There is a significant quadrupole background field from quadrupole magnet(s) even when these are unpowered.

• Based on rotating coil data, the remnant integrated quadrupole field could amount to a change in horizontal center by hundreds of microns, depending on quad position and the mode used for sextupole measurements.

• The vertical center measurement is not affected because By

(or Bx) is independent of y (or x) in a normal quadrupole field.

• Effectiveness of background correction has been tested by measuring a sextupole in the presence of a quadrupole which was either unpowered, or was powered at 2 A (apparent center shift of ~600 microns). Corrected center after background subtraction was within ±5 microns of the value without large background.



Alignment StabilityC26G4 returned from tunnel (Move 4_Repeated2)

-0.050

-0.040

-0.030

-0.020

-0.010

0.000

0.010

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5Magnet Position (m)

X-O

ffse

t fro

m B

est F

it (m

m)

Before Leaving (30-Sep)

Move3* (13-Oct-11)

Move4 (20-Oct-11)

Move4 (21-Oct-11)

* Move3 = As returned from the ring.Move 4 = All girder bolts torqued to 300 ft.lbs, then all bolts untorqued, except 3 corners.



Alignment StabilityC26G4 returned from tunnel (Move 4_Repeated2)

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

0.020

0.025

0.030

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5Magnet Position (m)

Y-O

ffse

t fro

m B

est F

it (m

m) Before Leaving (30-Sep)

Move3* (13-Oct-11)

Move4 (20-Oct-11)

Move4 (21-Oct-11)

* Move3 = As returned from the ring.Move 4 = All girder bolts torqued to 300 ft.lbs, then all bolts untorqued, except 3 corners.



Summary• A state-of-the-art vibrating wire system has been built for

aligning magnets for NSLS-II.• The system incorporates several novel features to improve and

ensure the accuracy of measurements (e.g., dual sets of sensors, recentering of sensors).

• Sources of errors have been studied in detail, and the measurements are tailored to minimize such errors.

• Excellent consistency and repeatability of measurements is demonstrated.

• System is being used successfully for aligning magnets on girders for NSLS-II, with 1/3 of multipole girders already completed.

Abstract

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